Coefficients of the poles of local zeta functions and their applications to oscillating integrals

2009/03/25 by Toshihisa Okada, Okada, Toshihisa, Kiyoshi Takeuchi +1
Mathematics · #11S90 #14P99 #46F15 #Algebraic Geometry (math.AG) #Complex Variables (math.CV) #FOS: Mathematics #math.AG #math.CV #msc:11S90 #msc:14P99 #msc:46F15

paper · pdf · doi:10.48550/arxiv.0903.4265

18 pages

arxiv created 2009/03/25 · arxiv updated 2009/12/01

Abstract

We introduce a new method which enables us to calculate the coefficients of the poles of local zeta functions very precisely and prove some explicit formulas. Some vanishing theorems for the candidate poles of local zeta functions will be also given. Moreover we apply our method to oscillating integrals and obtain an explicit formula for the coefficients of their asymptotic expansions.

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